# Correlation coefficient (method comparison)

A correlation coefficient measures the association between two methods.

The correlation coefficient is probably the most commonly reported statistic in method comparison studies. However, it is irrelevant for a number of reasons (Bland & Altman, 1986):

- It is a measure of the strength of linear association between two methods, the extent to which as one variable increases the other variable also tends to increase, not the agreement between them.
- A change in the scale of measurement does not affect the correlation, even though it affects the agreement. For example, if one method reports double the value of another method the correlation coefficient would still be high even though the agreement between the methods is poor.
- It simply represents the ratio of variation between the subjects relative to the measurement variation. The measuring interval chosen in study design can affect the correlation coefficient.

The correlation coefficient is sometimes re-purposed as an adequate range test (CLSI, 2002) on the basis that the ratio of variation between subjects, relative to measurement variation, is an indicator of the quality of the data (Stöckl & Thienpont, 1998). When the correlation coefficient is greater than 0.975 the parameters of an ordinary linear regression are not significantly biased by the error in the X variable, and so linear regression is sometimes recommended. However, with the wide range of proper regression procedures available for analyzing method comparison studies, there is little need to use inappropriate models.

**Related information**

- What is Analyse-it?
- What's new?
- Administrator's Guide
- User's Guide
- Statistical Reference Guide
- Distribution
- Compare groups
- Compare pairs
- Contingency tables
- Correlation and association
- Principal component analysis (PCA)
- Factor analysis (FA)
- Item reliability
- Fit model
- Method comparison / Agreement
- Correlation coefficient
- Scatter plot
- Fit Y on X
- Fitting ordinary linear regression
- Fitting Deming regression
- Fitting Passing-Bablok regression
- Linearity
- Residual plot
- Checking the assumptions of the fit
- Average bias
- Estimating the bias between methods at a decision level
- Testing commutability of other materials
- Difference plot (Bland-Altman plot)
- Fit differences
- Plotting a difference plot and estimating the average bias
- Limits of agreement (LoA)
- Plotting the Bland-Altman limits of agreement
- Mountain plot (folded CDF plot)
- Plotting a mountain plot
- Partitioning and reducing the measuring interval
- Agreement measures for binary and semi-quantitative data
- Chance corrected agreement measures for binary and semi-quantitative data
- Agreement plot
- Estimating agreement between two binary or semi-quantitative methods
- Study design
- Study design for qualitative methods
- Measurement systems analysis (MSA)
- Reference interval
- Diagnostic performance
- Survival/Reliability
- Control charts
- Process capability
- Pareto analysis
- Study Designs
- Bibliography

Version 6.10

Published 21-Jul-2022